The terahertz (THz) spectral range (f≈1-10 THz; λ≈30-300 micrometers; generally between the far-infrared and microwave bands) has long been devoid of efficient, narrowband and tunable semiconductor sources and, in particular, compact electrically-pumped room temperature semiconductor sources. For some time, a p-doped Germanium laser was the only available semiconductor source in the THz region; however, this source can only work at temperatures below that of liquid nitrogen (i.e., it requires cryogenic cooling).
Recently, semiconductor-based Quantum-Cascade Lasers (QCLs) have been developed for the THz spectral range with maximum operating temperatures in pulsed mode reported at 178 degrees Kelvin (with emission frequency at ˜3 THz). Nevertheless, some serious limitations are intrinsic to these lasers. First, their tunability is inherently limited due to the narrowness of the gain spectrum. Second, their operating temperature will likely remain restricted to cryogenic temperatures due to the fundamental requirement of population inversion across the low-energy THz transition; in particular, due to the narrow energy band transitions characteristic of THz radiation, as operating temperature increases there is more opportunity for non-radiative depletion of the higher energy state as additional channels of electron relaxation become available, thereby impeding population inversion. Alternative sources, based on photoconductive switches or mixer technology, can operate at room temperature but have low efficiency, large size and broad emission band.
In other research efforts involving QCLs, QCLs have been implemented to simultaneously lase at multiple different wavelengths in the mid-infrared spectral band (e.g., ˜5 to 10 micrometers). In one such example, a single quantum cascade active region simultaneously generated up to three different wavelengths, and in another example two active regions designed for mid-infrared generation at different wavelengths were integrated in a single QCL waveguide structure, from which two-wavelength generation was achieved at power levels of several hundred milliwatts.
Difference-frequency generation (DFG) is a nonlinear optical process in which two beams at frequencies ω1 and ω2 (often referred to as “pump” beams) interact in a medium with second-order nonlinear susceptibility χ(2) to produce radiation at frequency ω=ω1−ω2. The intensity of the wave at frequency ω=ω1−ω2 is given by the expression
                                          W            ⁡                          (                              ω                =                                                      ω                    1                                    -                                      ω                    2                                                              )                                ⁢                                    ω              2                                      8              ⁢                              ɛ                0                            ⁢                              c                3                            ⁢                              n                ⁡                                  (                                      ω                    1                                    )                                            ⁢                              n                ⁡                                  (                                      ω                    2                                    )                                            ⁢                              n                ⁡                                  (                  ω                  )                                                              ⁢                                                                  χ                                  (                  2                  )                                                                    2                    ×                                    W              ⁢                              (                                  ω                  1                                )                            ⁢                              W                ⁡                                  (                                      ω                    2                                    )                                                                    S              eff                                ×                      l            coh            2                          ,                            (        1        )            where lcoh=1/(|{right arrow over (k)}−({right arrow over (k)}1−{right arrow over (k)}2|2+(α/2)2) is the coherence length, W(ωi), n(ωi), and {right arrow over (k)}i are the power, refractive index, and the wave vector of the beam at frequency ωi, respectively, α stands for the losses at the difference frequency ω, Seff is the effective area of interaction, and it is assumed that the medium is transparent for both pumps and that the depletion of the pump powers in the DFG process may be neglected. It follows from Eq. (1) that, for efficient DFG, one, needs to use materials with large χ(2), input beams of high intensity, and achieve low losses and phase matching, |{right arrow over (k)}−({right arrow over (k)}1−{right arrow over (k)}2)≈0.
DFG may be employed to generate THz radiation by employing pump frequencies ω1 and ω2 in the infrared (IR) or visible spectral ranges, where good laser sources exist. Various research efforts have reported narrowband THz generation at room temperature by externally pumping nonlinear optical crystals such as LiNbO3 or GaAs with two continuous wave (CW) or pulsed lasers. One such effort reported CW THz generation based on DFG in LiNbO3pumped by the outputs from two laser diodes operating at wavelengths around 1.5 micrometers and power levels of approximately 1 W each, wherein the THz output could be tuned between 190 and 200 micrometers (1.5-1.6 THz). The output power of the detected THz signal was in the sub-nanowatt level. These efforts to generate THz radiation via DFG generally rely on low loss and phase matching in connection with the nonlinear medium to improve the conversion efficiency. In particular, they use focused beams from high-intensity pulsed solid-state lasers (usually ˜1 GW/cm2, often limited by the damage threshold of the nonlinear crystal) and achieve large coherence length of tens of millimeters by either true phase matching or quasi-phase matching in transparent nonlinear crystals. This approach offers broad spectral tunability and does work at room temperature; however it requires powerful laser pumps and a generally complicated optical setup, ultimately resulting in bulky and unwieldy THz sources.
According to Eq. (1), as the intensity of the signal produced in DFG is proportional to the square of the second-order nonlinear susceptibility, output power based on DFG could be greatly improved if nonlinear materials with higher second-order nonlinear susceptibilities are used. In this regard, research since the late 1980s has established that asymmetric single or coupled quantum well structures with significant optical nonlinearities in the mid- and far-infrared spectral regions can be engineered by tailoring respective energy levels associated with the quantum well structures to correspond with optical transitions within the same band, known as intersubband transitions. In particular, one study measured a second-order nonlinear susceptibility χ(2) of 106 pm/V (i.e., four orders of magnitude larger than that of traditional nonlinear crystals such as LiNbO3, GaP, GaAs, etc.) for DFG at 60 micrometers (5 THz) in coupled quantum-well structures.
The mechanism for the foregoing process is depicted in FIG. 1, wherein two mid-infrared beams from CO2 lasers emitting around 10 micrometers (respectively corresponding to energy transitions represented by the arrows 102 and 104) generate a difference-frequency signal at a wavelength of approximately 62 micrometers (corresponding to an energy transition represented by the arrow 106). In principle, such χ(2) would enable efficient THz generation even for relatively low pump intensities and low coherence lengths. However, high optical nonlinearity in these structures is achieved because all interacting fields are in resonance with the intersubband transitions. This results in strong absorption of the pump beams as well as the THz DFG beam, and thus unavoidably limits THz DFG efficiency.